Lipschitz and differentiability properties of quasi-concave and singular normal distribution functions

DOI10.1007/s10479-009-0598-0zbMath1227.60024OpenAlexW2127294592MaRDI QIDQ1958622

Werner Römisch, René Henrion

Publication date: 4 October 2010

Published in: Annals of Operations Research (Search for Journal in Brave)

Full work available at URL: http://edoc.hu-berlin.de/18452/8992

zbMATH Keywords

stochastic optimizationdifferentiabilityLipschitz continuityprobabilistic constraintsquasi-concave measuressingular normal distributions

Mathematics Subject Classification ID

Stochastic programming (90C15) Continuity and differentiation questions (26B05) Distribution theory (60E99) Distribution theory (60Exx)

Related Items

A discussion of probability functions and constraints from a variational perspective, A Gradient Formula for Linear Chance Constraints Under Gaussian Distribution, Gradient formulae for probability functions depending on a heterogenous family of constraints, Derivatives of probability functions: unions of polyhedra and elliptical distributions, Level bundle methods for constrained convex optimization with various oracles, A characterization of the subdifferential of singular Gaussian distribution functions, Gradient formulae for nonlinear probabilistic constraints with non-convex quadratic forms, Convergence analysis on a smoothing approach to joint chance constrained programs, (Sub-)Gradient Formulae for Probability Functions of Random Inequality Systems under Gaussian Distribution, Generalized differentiation of probability functions: parameter dependent sets given by intersections of convex sets and complements of convex sets

Uses Software

• QSIMVN

Cites Work

• Abstract tubes, improved inclusion-exclusion identities and inequalities and importance sampling
• Metric regularity and quantitative stability in stochastic programs with probabilistic constraints.
• Stability of Solutions for Stochastic Programs with Complete Recourse
• Improved bounds and simulation procedures on the value of the multivariate normal probability distribution function
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